AC current waveform Is there any reason one would choose a sine wave instead of a rectangular wave for example? What are the differences between them? Why would one prefer one waveform over the other in certain circumstances? I'm trying to understand why sometimes one form is used and another time a different one.
 A: Sine is more convenient: many physical problems are reduced to linear differential equations that have sines/cosines or exponentials as their solution, e.g. the generic equation for a linear oscillator is:
$$\frac{d^2x(t)}{dt^2} + \omega^2x(t)=f(t).$$ An LC circuit is also described by such an equation.
In addition, the Fourier analysis tells as that any periodic movement can be expanded in terms of siges and cosines (although other basis functions are possible). Note that rectangular wave has a special inconvenience of having badly defined first derivative.
A: A rotary AC alternator for AC power generation produces almost pure sine waves because of the fundamental geometry of its construction. So you get sine waves "for free". 
Square waves contain a significant amount of high frequency components in the "sharp" parts of its waveform, which the transformers used in high voltage AC power transmission cannot pass because of their inductance. So even if you could produce square waves instead of sine waves in some sort of generation scheme, the transformers would block a lot of the power content in them. This would be very inefficient. 
